Justifications in Calculus.

R(t) represents the rate at which people enter a line, measured in people per minute. What does R'(3) = 4 represent?

• At t = 3 minutes, people are entering the line at a rate of 4 people per minute.

• At t = 3 minutes, the rate at which people are entering the line is increasing at a rate of 4 people per minute per minute.

• At t = 3 minutes, there are 4 people in line.

• At t = 4 minutes, 3 people are in line.

L(t) represents the total number of lollipops that a class has eaten after t minutes. What does L'(10) = 12 represent?

• At t = 10 minutes, the class is eating lollipops at a rate of 12 lollipops per minute.

• At t = 10 minutes, the class has eaten 12 lollipops.

• At t = 10 minutes the rate at which the class is eating lollipops is increasing at a rate of 12 lollipops per minute per minute.

• At t = 12 minutes the class has eaten 10 lollipops.

M(t) represents the number of math problems your AP Calculus class has solved after t minutes.

What does M''(20) = -2 represent?

• At t = 20 minutes the rate at which the math class is solving problems is decreasing at a rate of 2 problems per minute per minute.

• At t = 20 minutes the rate at which the math class is solving problems is increasing at a rate of 2 problems per minute per minute.

• At 20 minutes, the math class is solving problems at a rate of 2 problems per minute.

• At 20 minuets the math class has solved -2 problems.

B(t) represents the temperature of the biscuits after t minutes. What does the following notation represent?

• The temperature of the biscuits at 10 minutes

• The average temperature of the biscuits on the time interval 3 to 10 minutes.

• The average rate of temperature on the interval 3 to 10 minutes.

• The change in temperature of the biscuits on the time interval 3 to 10 minutes.

B(t) represents the temperature of the biscuits after t minutes. What does the following notation represent?

• The temperature of the biscuits after 10 minutes.

• The average rate of the temperature of the biscuits on the time interval 3 to 10 minutes.

• The average temperature of the biscuits on the time interval 3 to 10 minutes.

• The temperature of the biscuits on the time interval 3 to 10 minutes.

A particle travels along the x-axis. The position of the particle at t = 4 is 10. Which of the following would give you the position of the particle at t = 7?

• 
• 
• v(7)

• v(4) + v(7)

A particle has a positive velocity and a negative acceleration. Which of the following is true?

• The speed is increasing.

• The speed is decreasing.

• The speed is neither increasing or decreasing.

• The particle is not moving.

A particle has a negative velocity and a negative acceleration. Which of the following is true?

• The speed is increasing.

• The speed is decreasing.

• The speed is neither increasing or decreasing.

• The particle is not moving.

The rate at which the temperature outside is changing is represented by the function O(t). What does the following represent?

• The temperature after 12 minutes is 15 degrees.

• The temperature has increased 15 degrees on the time interval 5 to 12 minutes.

• The rate of change of temperature on the interval 5 to 12 minutes is 15.

• The temperature at 5 minutes is 15 degrees.

H(t) represents the number of hats purchased at a store after t hours. What does the above notation represent ?

• The number of hats sold on the time interval 4 to 8 hours was 32.

• The number of hats sold at t = 8 hours was 32.

• The rate at which hats were sold on the interval 4 to 8 hours was 32.

• The number of hats sold at t = 4 hours was 32.